Method for channel estimation

ABSTRACT

A method of channel estimation is for a receiver to receive signals so as to estimate channel impulse response. The signal consists of a first data burst and a second data burst at least where a first training sequence and a second training sequence are interposed between the first data burst and the second data burst respectively. The channel estimation method comprises the following steps. First, estimating the channel impulse response of the first training sequence and the second training sequence respectively where each of the corresponding first channel impulse response and the corresponding second channel impulse response have n impulses so as to gather a first channel impulse response (A n ) and a second channel impulse response (B n ). Next, estimating channel impulse response (C n ) of a designated position of the data burst located between the first training sequence and the second training sequence. The channel impulse response (C n ) is estimated by using interpolation by convex function and taking channel impulse response (A n ) and (B n ) as end values.

BACKGROUND OF THE INVENTION

(1) Field of the Invention

The invention relates to a method for channel estimation, and moreparticularly to apply a quadratic function to simulate thecharacteristic of channel so as to mitigate the Doppler effect forchannel estimation.

(2) Description of the Prior Art

FIG. 1 illustrates the basic framework of wireless communication system.The communication system at least includes a transmitter 12 and areceiver 14. Each of the transmitter 12 and receiver 14 has its antenna16 and 18 for transmitting/receiving signals and then after a number ofsignal processing steps (such as demodulation, decoding, etc.) so as toget useful data. In the process from transmitter 12 to receiver 14,signals are propagated in channel 20. Ideally, the signal received fromthe receiver 14 should match the signal transmitted from the transmitter12.

Actually, the received signals will be affected by refraction orreflection with various objects over the channel 20 or with the relativeposition changing by transmitter and receiver during the signaltransmission. Therefore, the following phenomena might occurre inchannel 20 such as multi-path delay, fading, interference, etc. andfurther conclude signal distortion. Especially for mobile communicationsystem, the relative position of transmitter and receiver are changingfrequently that with different speed of moving receiver (or transmitter)results in different level of Doppler spread and causes more seriouslydistortion problem.

In order to simulate signals in channel transmission, some channelestimation method are adopted to adjust signals being affected inchannel so as to compensate the affected signal. In GPRS system, databursts are transported between a transmitter and a receiver. In FIG. 2,the data burst b1 in received signal may include Data 1, Data 2, and atraining sequence ts1 (contains 26 bit digital data) located betweenData 1 and Data 2 and data burst b2 has the same arrangement with databurst b1. It should be noted that ts1 and ts2 are predefined datarecognized by the receiver and transmitter. Hence, to compare thedifference of ts1 in receiver and in transmitter so as to estimate thechannel impulse response (CIR) in channel 20 and then with the CIR tocompensate Data 1 and Data 2 in data burst b1 and using the same rule toreceive Data 3 and Data 4 in data burst b2.

The more detail in prior art method shown in FIG. 3, in step 301,estimating CIR of training sequence ts1 and ts2 separately. For example,there are five taps of CIR A₁{grave over ( )} A₂{grave over ( )} . . .{grave over ( )} A₅ estimated from ts1 and B₁{grave over ( )} B₂{graveover ( )} . . . {grave over ( )} B₅ estimated from ts2 also referring toFIG. 2. Then in step 303, determining a predetermined position k locatedbetween ts1 and ts2 and estimating CIR of the position k. Next in step305, by using linear interpolation and substituting the end value A_(n)and B_(n) so as to get CIR(C_(n)) of the predetermined position k Asshown in FIG. 2, the first tap of CIR C₁ is determined by taking the endvalue of A₁ and B₁ using linear interpolation method and using the samerule to get C₂˜C₅.

Alternatively, we can divide the data burst into M parts and estimatecorresponding CIRs. In FIG. 2, Data 2 and Data 3 are divided into twoparts (M=2) separately, D2_1, D2_2 and D3_1, D3_2. And using theaforementioned method to get CIRs of every part.

Finally, in step 307, we use the estimated CIRs of each data burst toget data. FIG. 4 illustrates the functional block of estimating data ina receiver. We use the channel estimator 40 which is used for estimatingCIR of data burst by the aforementioned linear interpolation method andthe faded data received by the receiver so as to get more accurate datafrom the Viterbi equalizer 42.

However, the aforementioned prior art is not suitable in mobilecommunication system. This is because Doppler effect occurred in movingobjects and the aforementioned prior art has no concern about theDoppler effect. Therefore, in order to improve the foregoingdisadvantages, the present invention provides a channel estimationmethod which mentions about Doppler effect.

SUMMARY OF THE INVENTION

Accordingly, it is one object of the present invention to provide achannel estimation method by using a convex function (e.g. BesselFunction or quadratic function) to simulate the characteristic ofchannel so as to mitigate the Doppler effect.

Accordingly, it is one more object of the present invention to provide achannel estimation method to consider movement of a transmitter and areceiver so as to compensate the channel estimation error occurred byspeed.

The present invention provides a method for channel estimation utilizingin a receiver to receive signals, the signal comprises a first databurst and a second data burst where a first training sequence (ts1) anda second training sequence (ts2) are individually interposed in thefirst data burst and the second data burst, the channel estimationmethod comprises the following steps. Firstly, estimating channelimpulse responses (CIRs) of the ts1 and the ts2 where each of the ts1and the ts2 has n impulses so as to get a first CIR (A_(n)) and a secondCIR (B_(n)) respectively.

Subsequently, determining an interpolation number M of data burstlocated between the ts1 and the ts2, the predetermined position arelabeled as (d₁){grave over ( )} (d₂) . . . (d_(M)). Next, estimating aplurality of CIRs (C_(n1)){grave over ( )} (C_(n2)) . . . (C_(nM))according to the predetermined position (d₁){grave over ( )} (d₂) . . .(d_(M)), wherein the CIRs, (C_(n1)){grave over ( )} (C_(n2)) . . .(C_(nM)) valued by taking the first CIR (A_(n)) and the second CIR(B_(n)) as end value and using the convex function with thepredetermined position (d₁){grave over ( )} (d₂) . . . (d_(M)). Theconvex function can be simplified by a Bessel Function:C_(n)(d)=A_(n)×w_(n,0)(d)+B_(n)×w_(n,1)(d) where d is a predeterminedposition in data burst located within the ts1 and the ts2, C_(n)(d) is aCIR with the predetermined position, w_(n,0)(d) and w_(n,1)(d) areweight values calculated by the Bessel Function.

It should be noted that the weight value can be calculated be thefollowing equation:${w_{n}(d)} = {\frac{1}{{FF}\left( {2 - {FF}} \right)}\begin{bmatrix}{{{FF}\left( {1 - {X1}} \right)} - \left( {{X0} - {X1}} \right)} \\{{{FF}\left( {1 - {X0}} \right)} - \left( {{X1} - {X0}} \right)}\end{bmatrix}}$

-   -   , where        ${{FF} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{1} - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{X0} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{XI} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{1} - d} \right)}} \right\rbrack^{2}}{4}},{d_{0} \leq d \leq d_{1}},$        where f_(D) is Doppler frequency, T denotes time period between        received each data bit of the training sequence, and d denotes        scalar of the predetermined position (d=t/T). Moreover, the        convex function, F_(n)(x), the CIR can be written as:        C _(n)(d)=A _(n) ×F _(n,A)(d)+B _(n) ×F _(n,B)(d),        where F_(n,A)(d) and F_(n,B)(d) denote estimated CIRs at the        predetermined position d individually.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be specified with reference to itspreferred embodiment illustrated in the drawings, in which

FIG. 1 is a schematic view of basic framework for wireless communicationsystem;

FIG. 2 is a schematic view of composition of data burst transmitted inGPRS system;

FIG. 3 is a flow chart of prior art when receiving data in a receiver;

FIG. 4 is a function block about estimate data in a receiver;

FIG. 5 is a flow chart of receiving data in a receiver in accordancewith one embodiment with the present invention;

FIG. 6 is a schematic view of composition of data burst transmitted inGPRS system; and

FIG. 7A˜7C are compensation tables in different speed in accordance withone embodiment with the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The invention disclosed herein is a method for channel estimation, andmore particularly to apply a convex function to simulate thecharacteristic of channel so as to mitigate Doppler effect for channelestimation. In the following description, numerous details are set forthin order to provide a thorough understanding of the present invention.It will be appreciated by one skilled in the art that variations ofthese specific details are possible while still achieving the results ofthe present invention. In other instance, well-known components are notdescribed in detail in order not to unnecessarily obscure the presentinvention.

FIG. 5 illustrates a flow chart of receiving data in a receiver inaccordance with one embodiment with the present invention. Firstly,estimate channel impulse responses (CIRs) of the training sequences.Also referring to FIG. 6 which illustrates only two adjacent data burststransmitted in GPRS system where data bursts b3 may contain two data D5,D6 and a training sequence TS3 interposed between D5 and D6.Furthermore, data burst b4 may contain two data D7, D8 and anothertraining sequence TS4 interposed between D7 and D8 where D5, D6, D7, D8may store audio, video, audio/video or other digital data which maycontain 58 bits data.

However, for training sequence of data burst transmitted by transmitter,every training sequence of data burst contains the same digital data(could be contained 26 bits data). During signal transmission, thetraining sequence in each data burst may not similar any more. Forexample, we may decide to estimate five taps of CIR in each of TS3 andTS4 in order to find out the characteristic of transmission channel thatobtain channel response for data.

Subsequently, in step 503, we determine the interpolation number of databurst. In the present embodiment, we take the data (e.g. D6) and divideit into M segments to receive the corresponding data segments accordingto time. For example, to receive D6_0 at time d₁, and to receive D6_1 attime d₂ and so as D7_0 and D7_1. In this embodiment, each data isdivided into two data segments and received at four points (d1˜d4) oftime. Other kind of dividing rule according to bit number of data arewell known to the skilled person in the art and definitely any intent toinclude such a modification shall be within the scope of this invention.

The following step 505 of the present embodiment is to estimate CIR ofeach divided data segments by a convex function in accordance with apredetermined time position. During step 501, each five taps of CIR inTS3 and TS4 are estimated that the total ten taps of CIR are used forestimating CIR of each data segment (e.g. D6_0, D6_1, D7_0, and D7_1) bythe convex function where the convex function is simplified from aBessel Function. Each CIR, C_(n)(d) of data segment can be valued by thefollowing equation (1):C _(n)(d)=A _(n) ×w _(n,0)(d)+B _(n) ×w _(n,1)(d)  (1)

where d denotes a predetermined time position of data located betweenTS3 and TS4, and the estimated CIR at predetermined time positiondenotes C_(n)(d), w_(n,0)(d) and w_(n,1)(d) denote weight values inBessel Function. In the present embodiment, weight value wn(d) can befound in equation (2): $\begin{matrix}{{w_{n}(d)} = {\frac{1}{{FF}\left( {2 - {FF}} \right)}\begin{bmatrix}{{{FF}\left( {1 - {X1}} \right)} - \left( {{X0} - {X1}} \right)} \\{{{FF}\left( {1 - {X0}} \right)} - \left( {{X1} - {X0}} \right)}\end{bmatrix}}} & (2)\end{matrix}$where${{FF} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{1} - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{X0} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{XI} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{1} - d} \right)}} \right\rbrack^{2}}{4}},{d_{0} \leq d \leq d_{1}},$where f_(D) is Doppler frequency, T denotes time period between receivedof each data bit of training sequence, and d denotes scalar of thepredetermined time position (d=t/T), n denotes the received impulse withdifferent delay path, And the following description will illustrate howto get equation (2).

Firstly, In order to get optimum channel response, we have to findminimum square error (MSE) between actual channel responses andestimated channel responses by channel estimation. In other words, wecan find optimum weight value to make that square error is minimum. Weassume that the estimated CIR is C_(n)(d)=w_(n) ^(H)(d)C_(n). Accordingto MSE, which is function of the w_(n), we can use partial derivative,$\frac{\partial{ɛ_{n}(\mathbb{d})}}{\partial{w_{n}(\mathbb{d})}} = 0$to find out the optimum weight value for MSE. So, the minimum squareerror of Optimum Wiener Filter can be written as equation (3):ε_(n)(d)=E[|{overscore (C)} _(n)(d)−C _(n)(d)|²]  (3)where {overscore (C)}_(n)(d) denotes the ideal CIR, C_(n)(d) denotes theinterfered CIR, and C_(n)(d)=w_(n) ^(H)(d)C_(n), w_(n) ^(H)=[w_(n,0)(d)w_(n,1)(d)], then the value of MSE can be proved by the followingequations: $\begin{matrix}\begin{matrix}{{ɛ_{n}(d)} = {E\left\lbrack {{{{\overset{\_}{C}}_{n}(d)} - {C_{n}(d)}}}^{2} \right\rbrack}} \\{= {E\left\lbrack {\left( {{{\overset{\_}{C}}_{n}(d)} - {C_{n}(d)}} \right)\left( {{{\overset{\_}{C}}_{n}(d)} - {C_{n}(d)}} \right)^{H}} \right\rbrack}} \\{= {E\left\lbrack {{{{\overset{\_}{C}}_{n}(d)}{{\overset{\_}{C}}_{n}^{H}(d)}} - {{{\overset{\_}{C}}_{n}(d)}{C_{n}^{H}(d)}} - {{C_{n}(d)}{{\overset{\_}{C}}_{n}^{H}(d)}} + {{C_{n}(d)}{C_{n}^{H}(d)}}} \right\rbrack}} \\{= {{E\left\lbrack {{{\overset{\_}{C}}_{n}(d)}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack} - {E\left\lbrack {{{\overset{\_}{C}}_{n}(d)}{C_{n}^{H}(d)}} \right\rbrack} - {E\left\lbrack {{C_{n}(d)}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack} + {E\left\lbrack {{C_{n}(d)}{C_{n}^{H}(d)}} \right\rbrack}}} \\{= {\rho_{n} - {E\left\lbrack {{{\overset{\_}{C}}_{n}(d)}\left( {{w_{n}^{H}(d)}C_{n}} \right)^{H}} \right\rbrack} - {E\left\lbrack {\left( {{w_{n}^{H}(d)}C_{n}} \right){{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack} + {E\left\lbrack {\left( {{w_{n}^{H}(d)}C_{n}} \right)\left( {{w_{n}^{H}(d)}C_{n}} \right)^{H}} \right\rbrack}}}\end{matrix} & (4) \\\begin{matrix}{{{{if}\quad\rho_{n}} = {E\left\lbrack {{{\overset{\_}{C}}_{n}(d)}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack}},{then}} \\{{ɛ_{n}(d)} = {\rho_{n} - {{E\left\lbrack {{{\overset{\_}{C}}_{n}(d)}C_{n}^{H}} \right\rbrack}{w_{n}(d)}} - {{w_{n}^{H}(d)}{E\left\lbrack {C_{n}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack}} - {{w_{n}^{H}(d)}{E\left\lbrack {C_{n}C_{n}^{H}} \right\rbrack}{w_{n}(d)}}}} \\{= {\rho_{n} - {{Y^{H}(d)}{w_{n}(d)}} - {{w_{n}^{H}(d)}{Y(d)}} + {{w_{n}^{H}(d)}{{Xw}_{n}(d)}}}}\end{matrix} & (4.1)\end{matrix}$where Y=E[{overscore (C)}_(n)(d)C_(n) ^(H)(d)], X=E[C_(n) ^(H)(d)C_(n)^(H)(d)].

By partial derivative calculation with equation (4), the optimum weightvalue of winener filter is$\frac{\partial{ɛ_{n}(\mathbb{d})}}{\partial{w_{n}(\mathbb{d})}} = 0$and get 2Y(d)−2Xw_(n)(d)=0. Hence, the optimum wiener filter isw _(n)(d)=X ⁻¹ Y(d)  (5)

However, it is assumed that channel has characteristics of time variantand with multipath which corresponds to the situation of Wide SenseStationary Uncorrelated Scattering (WSSUS). Then the channel can bewritten in a form of Bessel Function, $\begin{matrix}{Y = {\begin{bmatrix}{E\left\lbrack {{C_{n}\left( d_{0} \right)}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack} \\{E\left\lbrack {{C_{n}\left( d_{5} \right)}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack}\end{bmatrix}\quad = {\begin{bmatrix}{E\left\lbrack {{{\overset{\_}{C}}_{n}\left( d_{0} \right)}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack} \\{E\left\lbrack {{{\overset{\_}{C}}_{n}\left( d_{5} \right)}{{\overset{\_}{C}}_{n}^{H}(d)}} \right\rbrack}\end{bmatrix}\quad = {\begin{bmatrix}{\beta\left( {d - d_{0}} \right)} \\{\beta\left( {d_{5} - d} \right)}\end{bmatrix}\quad = {\begin{bmatrix}{\rho_{n} \times {J_{0}\left( {2\pi\quad{f_{D}\left( {d - d_{0}} \right)}} \right)}} \\{\rho_{n} \times {J_{0}\left( {2\pi\quad{f_{D}\left( {d_{5} - d} \right)}} \right)}}\end{bmatrix}\quad}}}}} & (6) \\{{X = {{E\left\lbrack {C_{n}C_{n}^{H}} \right\rbrack} = \begin{bmatrix}{\rho_{n} + \upsilon_{n}} & {\beta\left( {d_{5} - d_{0}} \right)} \\{\beta\left( {d_{5} - d_{0}} \right)} & {\rho_{n} + \upsilon_{n}}\end{bmatrix}}}{{C_{n}(d)} = {{\begin{bmatrix}{w_{n,0}(d)} & {w_{n,1}(d)}\end{bmatrix}\begin{bmatrix}{C_{n}\left( d_{0} \right)} \\{C_{n}\left( d_{5} \right)}\end{bmatrix}} = {{w_{n}^{H}(d)}C_{n}}}}} & (7)\end{matrix}$

-   where ρ_(n)=E[{overscore (C)}_(n)(d){overscore (C)}_(n) ^(H)(d)]    denotes power of transmitted signal, υ_(n)=σ²/P denotes power of    noise signal, C_(n)(d₀)=A_(n) {grave over ( )} C_(n)(d₅)=B_(n)    represent the estimated CIR of TS3 and TS4 separately and will be    taken as end values in calculating CIRs of data segments located    between TS3 and TS4.

Although the optimum weight value can be calculated from equations (6)and (7), but known from equation (5), in order to obtain the optimumweight value, w_(n)(d), that we should calculate the inverse matrixincluded the Bessel Function which is known as a complex calculation.Hence, we use Taylor expansion to approximately solve the BesselFunction. Furthermore, according to the character of Bessel Function, weignore the order higher than second to reserve the part of quadraticfunction (e.g. convex function) with first order and second order so asto get the following equations: $\begin{matrix}{{w_{n,0}(d)} = {\frac{{{FF}\left( {1 - {X1}} \right)} - \left( {{X0} - {X1}} \right)}{{FF}\left( {2 - {FF}} \right)}w_{n,0}}} & (8) \\{{w_{n,1}(d)} = {\frac{{{FF}\left( {1 - {X0}} \right)} - \left( {{X1} - {X0}} \right)}{{FF}\left( {2 - {FF}} \right)}w_{n,1}}} & (9)\end{matrix}$where${{FF} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{5} - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{X0} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{XI} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{5} - d} \right)}} \right\rbrack^{2}}{4}},{d_{0} \leq d \leq d_{5}},{{w_{n,0}(d)}\quad{and}\quad{w_{n,1}(d)}}$denote the weight values of TS3 and TS4 which time positions are at d₀and d₅ individually.

When we substitute d=d₀ to the equations (6){grave over ( )} (7){graveover ( )} (8){grave over ( )} (9), and obtain the following equations:w _(n)(d ₀)=[w _(n,0) 0]  (10)Y(d ₀)=[ρ_(n)β(d ₅ −d ₀)]^(T)  (11)Y ^(H)(d ₀)w _(n)(d ₀)=ρ_(n)w_(n,0)  (12)w _(n) ^(H)(d ₀)Xw _(n)(d ₀)=(ρ_(n)+υ_(n))×(ρ_(n) w _(n,0))²  (13)Then according to the foregoing equations (10){grave over ( )} (11),(12){grave over ( )} (13) to obtain${w_{n,0} = \frac{\rho_{n}}{\rho_{n} + \upsilon_{n}}};$similarly, $w_{n,1} = \frac{\rho_{n}}{\rho_{n} + \upsilon_{n}}$can be obtained too, and substitute them to equations (8), (9) to get:$\begin{matrix}{{w_{n}(d)} = \begin{bmatrix}{w_{n,0}(d)} \\{w_{n,1}(d)}\end{bmatrix}} \\{= {\frac{\rho_{n}}{\rho_{n} + \upsilon_{n}}\begin{bmatrix}\frac{{{FF}\left( {1 - {X1}} \right)} - \left( {{X0} - {X1}} \right)}{{FF}\left( {2 - {FF}} \right)} \\\frac{{{FF}\left( {1 - {X0}} \right)} - \left( {{X1} - {X0}} \right)}{{FF}\left( {2 - {FF}} \right)}\end{bmatrix}}} \\{= {\frac{\rho_{n}}{\rho_{n} + \upsilon_{n}}{\frac{1}{{FF}\left( {2 - {FF}} \right)}\begin{bmatrix}{{{FF}\left( {1 - {X1}} \right)} - \left( {{X0} - {X1}} \right)} \\{{{FF}\left( {1 - {X0}} \right)} - \left( {{X1} - {X0}} \right)}\end{bmatrix}}}}\end{matrix}$If we ignore the effect of noise (to set υ_(n)=0), the near optimumweight value can be shown as follow:${w_{n}(d)} = {{\frac{1}{{FF}\left( {2 - {FF}} \right)}\begin{bmatrix}{{{FF}\left( {1 - {X1}} \right)} - \left( {{X0} - {X1}} \right)} \\{{{FF}\left( {1 - {X0}} \right)} - \left( {{X1} - {X0}} \right)}\end{bmatrix}}\quad\ldots\quad{same}\quad{with}\quad(2)}$

Therefore, the CIR compensated through the near optimum weight value inaccordance with the present invention can be obtained by the followingequation: $\begin{matrix}{{C_{n}(d)} = {\begin{bmatrix}{w_{n,0}(d)} & {w_{n,1}(d)}\end{bmatrix}\begin{bmatrix}{C_{n}\left( d_{0} \right)} \\{C_{n}\left( d_{5} \right)}\end{bmatrix}}} \\{= {{{C_{n}\left( d_{0} \right)} \times {w_{n,0}(d)}} + {{C_{n}\left( d_{5} \right)} \times {w_{n,1}(d)}}}} \\{= {{A_{n} \times {w_{n,0}(d)}} + {B_{n} \times {w_{n,1}(d)}\quad\ldots\quad{same}\quad{with}\quad(1)}}}\end{matrix}$where C_(n)(d₀) is A_(n), and C_(n)(d₅) is B_(n), which are estimatedfrom TS3 and TS4.

By way of the foregoing equations, the next step is to estimate CIRs bycorresponding weight values. As shown in FIG. 6, first, to estimatefirst tap of CIR for data segment (D6_0) at d₁ position according to thefirst CIR (A_(n), and B_(n)) of TS3 and TS4 at n=0 delay path and theweight values (by equations (8) and (9)), and the interpolation equation(1), the first CIR can be written as:C _(n)(d ₁)=A _(n)(d ₀)×w _(n,0)(d ₁)+B _(n) ×w _(n,1)(d ₁) . . . n=0,d=d ₁Similarly, to estimate the first tap of CIR for data segment (D6_1) atd₂ position in accordance with the CIRs of TS3 and TS4 at n=0 and theweight values, the data segment (D6_1) at d₂ can be written as:C _(n)(d ₂)=A _(n) ×w _(n,0)(d ₂)+B _(n) ×w _(n,1)(d ₂) . . . n=0, d=d ₂

After calculating CIRs of all data segments (D6_0˜D7_1) at n=0 delaypath, then follow up the foregoing steps described above to calculateother CIRs of data segments at different delay paths (n=1˜4).

Finally, in step 507, obtain the data of each data segments. Also,referring to FIG. 4, we use channel estimator 40 with the foregoingalgorithm in the receiver to estimate all CIRs of each data segment andcombine with the faded data received from antenna then through thearithmetic with Virterbe algorithm of equalizer 42 so as to compensatethe data distorted with speed.

FIG. 7A to FIG. 7C illustrate compensation tables withnon-interpolation, linear interpolation, optimum weight value, and nearoptimum weight value in different speed according to one embodiment withthe present invention. It should be noted that transmission durationtime in any data burst is about 577 microseconds and Doppler frequencyis about 42, 84, 334 Hz at speed of 50, 100, 400 km/hr separately. Toget values of every field in each table by normalizing the equation(4.1) written as follow:ε_(n)(d)=ρ_(n) −Y ^(H)(d)w _(n)(d)−w _(n) ^(H)(d)Y(d)+w _(n) ^(H)(d)Xw_(n)(d)  (4.1)normalize the equation (4.1) and get:${{\overset{\_}{ɛ}}_{n}(d)} = {\frac{ɛ_{n}(d)}{\rho_{n}} = {1 - \frac{{Y^{H}(d)}{w_{n}(d)}}{\rho_{n}} - \frac{{w_{n}^{H}(d)}{Y(d)}}{\rho_{n}} + \frac{{w_{n}^{H}(d)}{{Xw}_{n}(d)}}{\rho_{n}}}}$from equation (5): w_(n)(d)=X⁻¹Y(d) and get: $\begin{matrix}\begin{matrix}{{{\overset{\_}{ɛ}}_{n}(d)} = {1 - \frac{{Y^{H}(d)}X^{- 1}{Y(d)}}{\rho_{n}} - \frac{{Y^{H}(d)}X^{- 1}{Y(d)}}{\rho_{n}} + \frac{{Y^{H}(d)}X^{- 1}{Y(d)}}{\rho_{n}}}} \\{= {1 - \frac{{Y^{H}(d)}X^{- 1}{Y(d)}}{\rho_{n}}}} \\{= {1 - {{w_{n}^{H}(d)}\frac{Y(d)}{\rho_{n}}}}} \\{= {1 - {\begin{bmatrix}{w_{n,0}(d)} & {w_{n,1}(d)}\end{bmatrix}\begin{bmatrix}{J_{0}\left( {2\pi\quad{f_{D}\left( {d - d_{0}} \right)}} \right)} \\{J_{0}\left( {2\pi\quad{f_{D}\left( {d_{5} - d} \right)}} \right)}\end{bmatrix}}}} \\{= {1 - {{w_{n,0}(d)} \times {J_{0}\left( {2\pi\quad{f_{D}\left( {d - d_{0}} \right)}} \right)}} + {{w_{n,1}(d)} \times {J_{0}\left( {2\pi\quad{f_{D}\left( {d_{5} - d} \right)}} \right)}}}}\end{matrix} & (14)\end{matrix}$

According to the foregoing conditions (such as transmission durationtime of data burst, Doppler frequency, etc.) and weight valuescalculated by different ways (e.g. non-interpolation, linearinterpolation, optimum weight values, and near optimum weight values)and substitute to equation (14) so as to get every values of field intables of FIG. 7A to FIG. 7C. As shown in values of tables, the weightvalues using near optimum weight has a relatively small error compare tothe weight values using linear interpolation of prior art technology.

It should be noted that in the foregoing embodiment, we use TS3 and TS4of data burst b3 and b4 to get data D6 and D7. Moreover, data D5 of databurst b3 and D8 of data burst b4 should be utilized by the front sidetraining sequence of data burst b3 (maybe b2, but not shown) and theback side training sequence of data burst of b4 (maybe b5, but notshown) and using the method disclosed in the present invention so as toget all data of each data burst.

While the preferred embodiments of the present invention have been setforth for the purpose of disclosure, modifications of the disclosedembodiments of the present invention as well as other embodimentsthereof may occur to those skilled in the art. Accordingly, the appendedclaims are intended to cover all embodiments which d0 not depart fromthe spirit and scope of the present invention.

1. A method of channel estimation in a receiver to receive signals, thesignal comprises a first data burst and a second data burst where afirst training sequence (ts1) and a second training sequence (ts2) areindividually interposed in the first data burst and the second databurst, the channel estimation method comprises the steps of: estimatingchannel impulse responses (CIRs) of the ts1 and the ts2 where each ofthe ts1 and the ts2 has n impulses so as to get a first CIR (A_(n)) anda second CIR (B_(n)) respectively; and estimating CIR of a predeterminedposition of data burst located between the ts1 and the ts2, saidestimated CIR includes n impulses valued (C_(n)) separately, said(C_(n)) valued by taking the first CIR (A_(n)) and the second CIR(B_(n)) as end value and using a convex function with the predeterminedposition.
 2. The channel estimation method according to claim 1, furthercomprising the steps of: determining an interpolation number M of databurst located between the ts1 and the ts2, the predetermined positionare labeled as (d₁){grave over ( )} (d₂) . . . (d_(M)); estimating aplurality of CIRs (C_(n1)){grave over ( )} (C_(n2)) . . . (C_(nM))according to the predetermined position (d₁){grave over ( )} (d₂) . . .(d_(M)) wherein the CIRs, (C_(n1)){grave over ( )} (C_(n2)) . . .(C_(nM)) valued by taking the first CIR (A_(n)) and the second CIR(B_(n)) as end value and using the convex function with thepredetermined position (d₁){grave over ( )} (d₂) . . . (d_(M)).
 3. Thechannel estimation method according to claim 1, wherein the convexfunction is a Bessel Function,C_(n)(d)=A_(n)×w_(n,0)(d)+B_(n)×w_(n,1)(d) where d is a predeterminedposition in data burst located within the ts1 and the ts2, C_(n)(d) is aCIR with the predetermined position, w_(n,0)(d) and w_(n,1)(d) areweight values calculated by the Bessel Function.
 4. The channelestimation method according to claim 3, wherein position of the ts1 islabeled as d₀, and position of the ts2 is labeled as d₁, the weightvalue,${w_{n}(d)} = {\frac{1}{{FF}\left( {2 - {FF}} \right)}\begin{bmatrix}{{{FF}\left( {1 - {X1}} \right)} - \left( {{X0} - {X1}} \right)} \\{{{FF}\left( {1 - {X0}} \right)} - \left( {{X1} - {X0}} \right)}\end{bmatrix}}$ where${{FF} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{1} - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{X0} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d - d_{0}} \right)}} \right\rbrack^{2}}{4}},{{X1} = \frac{\left\lbrack {2\pi\quad f_{D}{T\left( {d_{1} - d} \right)}} \right\rbrack^{2}}{4}},{d_{0} \leq d \leq d_{1}},$where f_(D) is Doppler frequency, T denotes time period between receivedeach data bit of the training sequence, and d denotes scalar of thepredetermined position (d=t/T).
 5. The channel estimation methodaccording to claim 1, wherein the convex function, F_(n)(x), the CIR canbe written as:C _(n)(d)=A _(n) ×F _(n,A)(d)+B _(n) ×F _(n,B)(d), where F_(n,A)(d) andF_(n,B)(d)denote estimated CIRs at the predetermined position dindividually.
 6. The channel estimation method according to claim 1,wherein the data burst contains 58 bits data.
 7. The channel estimationmethod according to claim 1, wherein the training sequence within thedata burst contains 26 bits data.
 8. The channel estimation methodaccording to claim 1, wherein n ranges from 0 to
 4. 9. The channelestimation method according to claim 1, wherein the channel estimationmethod is applied in GPRS system.
 10. The channel estimation methodaccording to claim 1, wherein data of the data burst belongs to audiodata.
 11. The channel estimation method according to claim 1, whereindata of the data burst belongs to video data.
 12. The channel estimationmethod according to claim 1, wherein data of the data burst belongs toaudio and video data.